Study design and setting
Surveys (DHS) conducted in four SSA countries: DR Congo DHS (2013/14 DRCDHS), Ethiopia DHS (2016 EDHS), Nigeria DHS (2018 NDHS), South Africa DHS (2016 SADHS). The DHS is cross-sectional in design and provide population-based health indicators to assist policymakers and programme managers in designing and evaluating programs and strategies for improving the health of a country's population. The data, collected by trained field workers, contain self-reported information on the sexual and reproductive health history of the sampled women.
Currently, the four countries have diverse population sizes: DR Congo (90 million), Ethiopia (115 million), Nigeria (206 million) and South Africa (60 million); these constitute the largest population in middle, eastern, western, and southern regions of SSA [1], respectively. Of note, these countries are among the nine countries of the world projected to house more than 50% of the global population increase by 2050, except for South Africa [4]. The growth rates and TFR in DR Congo are respectively 3.5 and 6.2; Ethiopia, 2.7 and 4.3; Nigeria, 2.5 and 5.3; and South Africa, 1.1 and 2.3 [1]. Although South Africa fertility rate remains the lowest in sub-Saharan Africa, her observed fertility decline is still above the replacement level. Furthermore, these countries are classified as low-middle-income countries by the World Bank. Nigeria and South Africa are the two leading economic countries in the continent rated as middle-income; Ethiopia and DR Congo are rated as low-income countries.
In these countries, the DHS employs a stratified two-stage cluster sampling technique using the sampling frame containing the enumeration areas (EAs). In the first stage, clusters (otherwise known as EAs) are selected using a probability proportional-to-size approach per stratum. At the second stage, households are selected as the secondary sampling units using a systematic sampling per cluster. Women of childbearing age who reside in the respective countries were the study participants. A detailed description of the sampling design and strategies has been previously reported [32,33,34,35].
Study population and variables
Of the 18,827, 15,683, 41,821, 8514 women aged 15–49 years who participated in the 2014 DRCDHS, 2016 EDHS, 2018 NDHS, 2016 SADHS respectively, 13,884, 10,114, 29,296, 6039 had had at least one birth and were included in the current study. These were the participants who had reported at least one singleton childbirth as of the survey date.
Outcome variable The dependent variable of interest was the time elapsed between first and second childbirth among women in the selected countries. Women who did not have second childbirth as at the time of the survey were right-censored and were coded 0; otherwise, 1 in the analysis.
Independent variables The key independent variables were contraceptive use and fertility desire. Use of contraceptive was derived from the questions asking women to indicate “whether they ever used anything or tried to delay or avoid getting pregnant” and their “current contraceptive use by method type”; this was categorised as “never-, former-, or current-use” of any means to delay/stop pregnancy/childbirth. Fertility desire, derived from the questions asking women to indicate whether they desired more children were re-categorised as “no-more, want, or undecided”. Based on existing empirical studies [16, 36], other covariates considered for the study were ethnicity, religion (Christianity, Islam, traditionalist/other), education (none, primary, secondary, tertiary), wealth index (low, middle, high), age (< 20, 20–24, ≥ 25 years) and marital status at-first-birth (never married, married before first-birth, married after first-birth), employment status (not working, working), first-birth sex (male, female) and first-birth survival (dead, alive). Of note, the wealth index variable, derived from the generated weighted factor score by principal component analysis as contained in the women recode file, was grouped into low, middle, and high wealth quintiles. It is a proxy measure of household socio-economic status due to the non-existence of information on household income. The term ethnicity indicated self-reported ethnic group in each of the country except South Africa, where information on skin colour was provided. Also, the information on religion was unavailable in the 2016 SADHS.
Statistical data analysis
Survival analysis methods were used for the analysis. The “failure time” for women who have had second birth was the SBI. The “censored time” for the women without second birth yet was time since the first-birth and interview date. The Kaplan–Meier survival method was used to describe the women’s time to second birth while the log-rank test was employed to examine the association between SBI duration and the individual explanatory variables. Semi-parametric Cox proportional hazard (CPH) regression was thereafter used to evaluate the effect of contraceptive use and fertility desire on SBI amidst other variables controlled for, in each of the selected countries.
Model expression The CPH model can be written as:
$$h\left( {t_{i} } \right) = h_{0} \left( t \right)\ell^{{\sum\nolimits_{j = 1}^{p} {b_{j} x_{ji} } }} \,\mathop{\longrightarrow}\limits^{imlying}\,\ln \frac{{h\left( {t_{i} } \right)}}{{h_{0} \left( t \right)}} = \mathop \sum \limits_{j = 1}^{p} b_{j} x_{ji}$$
(1)
where \({b}_{j}\)—jth coefficients of the explanatory variable Xj, p—number of explanatory variables, \({h}_{0}\left(t\right)\)—baseline hazard function such that \({\mathrm{h}\left(t\right)/h}_{0}\left(t\right)\)—indicates the hazard ratio (HR), and the conditional probability of experiencing second childbirth within a short time interval (t, t + ∆t) having survived till time t is
$$h\left( t \right) = \mathop {{\text{lim}}}\limits_{\Delta t \to 0} \left\{ {\frac{{P\left( {t \le T \le t + \Delta t\left| T \right\rangle t} \right)}}{\Delta t}} \right\}$$
(2)
Usually, the relationship between hazard, H(t) and survival, S(t) functions is expressed as
$$S\left( t \right) = e^{ - H\left( t \right)}$$
(3)
where
$$S\left( t \right) = \mathop \smallint \limits_{t}^{\infty } f\left( y \right)dy = P\left( {T > t} \right) = 1 - F\left( t \right)$$
(4)
$$F\left( t \right) = \mathop \smallint \limits_{0}^{t} f\left( y \right)dy = P\left( {T < t} \right)$$
(5)
The F(t) is the cumulative probability that a woman has her second birth before time t; f(t) is the probability density function of the survival time T, defined as the probability that a woman has her second childbirth per unit time in a short interval expressed as:
$$f\left( t \right) = \mathop {{\text{lim}}}\limits_{\Delta t \to 0} \left\{ {\frac{{P\left( {t \le T < t + \Delta t} \right)}}{\Delta t}} \right\}$$
(6)
If ni is the number of women who were exposed to the risk of having second birth, censored women inclusive, before ith survival time (ti) and li is the number of women who had second birth at ti, then Eq. (7) below estimates the survival functions.
$$s\left( t \right) = \mathop \prod \limits_{i = 1}^{m} \left\{ {\frac{{n_{i} - l_{i} }}{{n_{i} }}} \right\} \mathrel\backepsilon t_{m} < t < t_{m + 1} ;\quad s\left( t \right) = 1\,if\,t < t_{1}$$
(7)
where m is the number of different failure times (i.e., experiencing second birth).
The unadjusted CPH model was used to explain the association between each of the main independent variables including the other covariates and SBI. Using the Wald test to assess the significance of the interplay between the key variables (contraceptive use and fertility desire), the statistically significance of the interaction term was not uniform across the studied countries (this was not presented). Thus, having confirmed non-violation of the proportional hazard assumption, two adjusted CPH models were fitted. Model 1 constitutes only the key independent variables and model 2 includes all the significant variables (p < 0.15) based on the log-rank test in addition to the main independent variables. The Wald test using the deviance statistic, − 2log likelihood (− 2LL), was used to select the best model with the least value being adjudged as more adequate.
The hazard ratios (HR) including their 95% confidence intervals are reported. The exponentials of the coefficients (bj which indicates the changes in the expected time to second birth due to a unit change in the jth predictor) suggest the tendency of hazard to second birth; thus, HR > 1 indicates higher hazard and HR < 1 lower hazard. The data was weighted to adjust for differences in population sizes of each region of the selected countries. All analyses were carried out at a 5% level of significance, using STATA 14 SE.
Ethical considerations
Ethical approval for the parent study was obtained from the National Ethics Committee in the respective countries and the ICF Institutional Review Board. The details of the ethical approval have been reported earlier [32,33,34,35]. The present study analysis utilised a secondary dataset, freely available for use in the public domain, which requires no ethics approvals. Meanwhile, the Demographic and Health Surveys Program authorised the utilisation of the dataset for the present analysis.
